The Fast Fourier Transform (FFT) is used in finding the correct frequency components of a signal that has been affected with noise.Frequency leakage is spreading of spectrum, because discrete Fourier Transform (DFT) can solve accurate only frequencies of integer multiples of sampling period fundamentals. Effects of leakage can be reduced by using window functions on input data sequence. These functions reduce level of the samples near edges of sampling period close to zero, which smoothes discontinuities of reproduced signal. Performance of the different window functions can be best analyzed from the frequency response which consists of one main lobe and several side lobes. Selection of a suitable window function is always a compromise between good frequency resolution and leakage behaviour. This thesis describes some fast algorithms for DFT and some common window functions for reducing the frequency leakage. Additionally, properties of the different algorithms and window functions are considered. The frequency spectrum analyzer implementations using a proper FFT-algorithm with suitable window functions are also considered. Finally, the introduced and designed frequency spectrum analyzer implementation is tested in both motor laboratory and real power plant environment.